Densitometer

ABSTRACT

A vibration densitometer having means for producing an output signal which is a pulse train of a pulse repetition frequency that is the function of the density of a fluid in which a densitometer probe is immersed. The densitometer has a linearization circuit which is exceptionally accurate for both liquid and gas density measurement or the like, the linearization circuit producing an output voltage Eoo given by the equation Eoo AT2 + CT + B, where A, B and C are constants, and T is the reciprocal of the pulse repetition frequency.

United States Patent (1 1 l m 3,769,831

Schiatter 1\ Nov. 6, 1973 DENSITOMETER 3,426,593 2/l969 Jacobs 73 32 x Inventor: Gerald Lance Schiatter, e 3,444,723 5/1969 Wakefield 73/32 Colo. I Primary Examiner-Richard C. Queisser Asslgnee! lntel'natlonal Telephfme and Assistant ExaminerArthur E. Korkosz p 'p New York, Attorney-C. Cornell Remsen, Jr. et al. NY. 7

[22] Filed: Oct. 13, 1971 [57] ABSTRACT [21] Appl. No.: 188,888 y A vibration densitometer having means for producing 7 an output signal which is a pulse train of a pulse repetition frequency that is the function of the density of a 5 E 3 U S Cl zgjg fluid in which a densltometer probe IS immersed. The [58] Field of Search 73/32 densitometer has a linearization circuit which is excepv tionally accurate for both liquid and gas density mea- 56] References Cited surement or the like, the linearization circuit producing an output voltage E given by the equation E AT UNITED T PATENTS CT B, where A, B and C are constants, and T is the 2,635,462 POdG et al. 73/32 reciprocal of the pulse repetition frequency. 3,117,440 [H964 wilnel' 3,307,408 3/1967 Thomas et al. 73/462 6 Claims, 19 Drawing Figures r\ 4 L 1.- /4 .53 w I w! 1 1" 62 5 6 y l I 54 l as A 5a a 55 i 2/ i V L, [a 42 r i /i PATENIEI] NEW 6 I975 SHEETIIUFY I I I I I I I I I FROM PR5 QMP .SUPPLV go; FIG. 5

'PATENTEnnav a ma 3,769,831

SHEET 70F 7 r 1 T i i l V I I I w; IIIIIHIIIIH ummmmmum l 1 I CONNECTED FROM 5/5 LEAD 6Q //v H6. /5

CONNECTED FROM OUTPUT OF flMPL/F/ER 37 /N CONNECTED TO INPUT LEZJD .500

1 DENSITOMETER The benefit of the filing dates of two copending applications is hereby claimed for this application. These two copending applications are Ser. No. 65,371 filed Aug. 20, 1970, for DENSITOMETER by C. E. Miller and G. L. Schlatter The other of the said two copending applications is Ser. No. l3l,l3l filed Apr. 5, 1971, for DENSITOMETER AND CALIBRATION METHOD AND APPARATUS THEREFOR by G. L. Schlatter.

BACKGROUND OF THE INVENTION This invention relates to devices for determining the density of a fluid, and more particularly, to apparatus for producing an output signal directly proportional to fluid density.

In the past, it has been very difficult to produce an analog signal directly proportional to the density of a gas.

SUMMARY OF THE INVENTION In accordance with the device of the present invention, the above described and other difficulties of the prior art are overcome by providing an analog device for producing an output signal, E whereE AT CT B, T is the reciprocal of the resonant frequency of the vibration densitometer of the present invention and A, B and C are constants.

The signal E is then directly proportional to the density of the fluid in which the densitometer vibrating structure is submerged.

The above-described and other advantages of the present invention will be better understood from the following detailed description when considered in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS In the drawings which are to be regarded as merel illustrative:

FIG. 1 is a perspective view of a densitometer probe constructed in accordance with the present invention;

FIG. 2 is a sectional view of the probe taken on the line 2-2 shown in FIG. 1;;

FIG. 3 is' a perspective view of a group of component parts of the probe shown in FIG. 1;

FIG. 4 is a transverse sectional view of the assembly taken on the line 4--4 shown in FIG. 3;

FIG. 5 is an enlarged longitudinal sectional view of a portion of the probe shown in FIG. 1;

FIG. 6 is a longitudinal sectional view of a portion of mounting means for an electrical connector otherwise substantially fixed relative to the probe taken on the line 6-6 shown in FIG. 2; 1

FIG. 7 is a block diagram of a densitometer constructed in accordance with the present invention;

FIG. 8 is a schematic diagram of a crystal, an input circuit, an amplifier, a squarer, a selfstart oscillator, a synchronous detector, and a differentiator shown in FIG. 7;

FIG. 9 is a schematic diagram of a tracking filter, an amplifier, a filter frequency control circuit, a phase detector, a squarer, a driver amplifier, and a driver coil shown in FIG. 7;

FIG. 10is a schematic diagram of a circuit illustrated as a switch in FIG. 7;

FIG. 11 is a more detailed block diagram of a linearization circuit shown in FIG. 7;

FIG. 12 is a block diagram of a. pulse former circuit shown in FIG. 11; I

FIG. 13 is a block diagram of ,a predetermined counter shown in FIG. 12;

FIGS. 14 and 15 are schematic diagrams of integrators shown in FIG. 11;

FIG. 16 is a schematic diagram of a sample and hold circuit shown in FIG. 11;

FIGS. 17 and 18 are graphs of groups of waveforms characteristic of the operation of the invention; and FIG. 19 is a schematic diagram of an additional portion of a linearization circuit shown in FIG. 7.

DESCRIPTION OF THE PREFERRED EMBODIMENT THE PROBE OF FIG. 1

In FIG. 1, a vibration densitometer probe 10 is shown having a shank 11, a housing 12 at its upper end, a tubular assembly 13 at its lower end, and an electrical connector assembly 14 at the upper end of housing 12 fixed thereto by bolts 15'. Annular fittings l6 and 17 extend around shank 11 for mounting probe 10 in a hollow cylindrical extension 18 of pipeline 19, as shown in FIG. 2.

As shown in FIGS. 1 and 2, a stainless steel vane 20 is mounted in assembly 13 in a position perpendicular to the axis of a hollow cylindrical magnetostrictive inner tube 21'. Vane 20, if desired, may be also mounted in a symmetrical position with respect to the axis of an outer sleeve 22 which houses it.

Vane 20 may be a rectangular plate having flat and parallel upper and lower surfaces as shown in FIG. 2, and may otherwise have mutually normal surfaces forming a right parallelopiped.

Shank 11 not only includes inner tube 21', but an outer magnetic tube 23'. A driver coil or solenoid winding 24' wound on a nylon bobbin 25' is press fit onto the external surface of inner tube 21 and located in a space between the tubes 21' and 23' toward the lower end of shank 11'. Coil 24' is thus maintained in a substantially fixed position on inner tube 21', al-. though the same is not necessarilypritical to the operation of the device of the present invention.

Vane 20 is supported between two half cylinders 26 and 27 as shown in FIGS. 2 and 3.According to the invention, the longitudinal edges of vane 20' are pressed together between half cylinders 26' and-27 with a pressure of, for example, 20,000 pounds per square inch because the assembly shown in FIG. 3 is inserted in sleeve 22' with an interference fit, sleeve 22' being heated prior to the said insertion. A workable alternative is to electron beam weld vane 20' to half cylinders 26' and 27'.'The welded assembly may then also be subjected to pressure by the said interference fit. However, the following description relates to the unwelded alternative.

Half cylinder 26' has four projections 28', and half cylinder 27' has four projections 29'. Projections 28' and 29' serve to prevent longitudinal movement of vane 20' between half cylinder 26 and half cylinder 27' although the same is not likely due to the clamping pressure on vane 20' between half cylinder 26' and half cylinder 27'.

Half cylinders 26' and 27', and vane 20 may be machined to have a flat or recess to receive a piezoelectric crystal 30'. Crystal 30' has electrical leads 31' and 3 2 which extend around half cylinders 26' and 27 in grooves 33' and 34', respectively, to a point where they enter the hollow interior of inner tube 21'. This entry is made at the lower end of inner tube 21', as shown in FIG. 2.

As shown in FIG. 3, projections 28' and 29' may have a slight separation at 35 to insure that the pressure contact of half cylinders 26 and 27' on vane 20 is quite high due to the said interference fit.

As shown in FIG. 2, a boss 36' is welded at 37 to sleeve 22 in a fluid tight manner. Although the device of the present invention need not always be fluid tight throughout, a glass-to-metal seal or other seal may be provided inside inner tube 21' for leads 31' and 32. Before the said interference fit is provided, if desired, crystal 30, and those portions of leads 31' and 32 in grooves 33' and 34', respectively, may be potted with an epoxy. Further, after the interference fit has been effected, the entire unit when completely assembled may be treated further by applying a bonding agent around all of the structures inside sleeve 22'. Any conventional bonding process may be employed including, but not limited to, the application of a bonding agent sold under the tradename of Locktite.

As stated previously, boss 36' may be welded to sleeve 22' at 37 in a fluid tight manner. Further, outer tube 23 may be threaded onto boss 36' and welded thereto at 38 in a fluid tight manner. For all practical purposes, boss 36' may thus be considered an integral part of outer tube 23'. Boss 36', for example, is also made of a magnetic material. All of the magnetic materials" referred to herein may be any magnetic material including, but not limited to, stainless steel. However, inner tube 21, although being magnetic, is also magnetostrictive. It is to be noted, however, that inner tube 21' is employed to produce vibration.

Inner tube 21 has an annular projection 39 with a shoulder 40'. Outer tube 23 has a lower bore 41' separated from a smaller upper counter bore 42' by an annular shoulder 43'. Shoulders 40' and 43 abut. From shoulder 40' to the lower end of inner tube 21', inner tube 21' is always in axial compression. That is, inner tube 21' is in compression when coil 24 is either energized or deenergized. Coil 24 is energized with a level shifted sine wave current which thus merely changes the degree of compression of inner tube 21. The current always flows in one direction. The energizing voltage may typically be a level shifted sine wave having an average value of 0.1 volt and maximum excursions of +25.l volts and 24.9 volts.

Projection 39' has a hole 44 through which the electrical leads of coil 24' can pass from the location of coil 24' upwardly between tubes 21' and 23'. I

The manner in which probe is mounted in pipeline 19 is better illustrated in FIG. 5. In FIG. 5, note will be taken that outer tube 23' has an outwardly extending radial projection 45' on each side of which rubber O-rings 46' and 47 are compressed by fittings 16' and 17'. Fitting 17' is threaded into extension 18' and sealed thereto by a conventional sealing component 48' shown in FIG. 2. In FIG. 5, note will be taken that fitting 16' is threaded inside fitting 17 at 49'. The amount O-rings 46 and 47 are compressed is, therefore, determined by the position of fitting 16. That is, fitting 16' isg'turned, for example, by a wrench, until the desired O-ring compression is reached.

From the construction illustrated in FIG. 5, note will be taken that only O-rings 46' and 47 contact outer tube 23', and that, therefore, shank 11' is never touched by either fitting 16' or fitting 17 It is an advantage of the present invention that the construction of probe 10 is such that the leads from coil 24' are kept magnetically separate from the leads from crystal 30 in at least a portion of housing 12' as will be described. Housing 12' has a fitting 50'threaded onto outer tube 23. A cylinder 51' is threaded to fitting 50'. A washer 52 is press fit and thereby fixed in fitting 50 and around inner tube 21. Inner tube 21' has an upper end which may be fixed relative to or slidable in washer 52, as desired. However, preferably the external surface of inner tube 21 at its upper end fits contiguous to or in contact with the surface of washer 52' defining the hole therethrough. A shield 53 made of a magnetic material may be fixed around fitting 50 by one or two or more screws 54. Outer tube 23 has a radial hole 55 therethrough through which the leads from coil 24 pass. Fitting 50 has a hole 56' therethrough in alignment with hole 55 through which the leads from coil 24 pass.'From the outward radial extremity of hole 56', the coil leads indicated at 57 and 58' pass upwardly between cylinders 51' and shield 53 and are connected to pins 59 and 60 of the electrical connector 14. Electrical connector 14' may be a conventional five pin connector.

As stated previously, the leads 31' and 32 from crystal 30 extend upwardly through the interior of inner tube 21. At the upper end of inner tube 21 as shown in FIG. 2, leads 31 and 32 are connected to the input of differential amplifier 61. Leads 31 and 32' thus extend outwardly through the upper opening in inner tube 21.

Differential amplifier 61 may be entirely conventional, and mounted on a conventional card, if desired. Amplifier 61' may be supported inside shield 53' by any conventional means, if desired, or simply supported by the strength of leads 31' and 32', and output leads 62' and 63' which are connected to pins 64 and 65' of connector 14, respectively. A lead 66' provides a ground connection from shield 53' to the fifth pin 67' of connector 14.

The manner in which connector 14' is mounted on cylinder 51' is shown in FIG'. 6. Only one bolt 15 is shown in FIG. 6 since all bolts 15 are similarly situated. In FIG. 6, bolt 15' is shown having a head 68', a washer 69' under head 68', an O-ring 70 under washer 69', and a shank 71' threaded into cylinder 51. A second O-ring 72 also extends around screw shank 71'. O-ring 70 fits between the lower surface of washer 69' and a countersunk frusto-conical hole 73' in connector 14. O-ring 72' fits between the upper surface of cylinder 51 and another counter sunk frusto-conical hole 74' in connector 14'. Holes 73' and 74' are connected by a bore 75 From FIG. 6, it will be noted that all the structures shown therein may vibrate, but that the amount of vibration transmitted to connector 14' may be quite small. However, several features of the present invention are not limited to this construction.

THE DENSITOMETER OF FIG. 7

In FIG. 7, probe 10' is shown including a magnetostrictive driver 104, vane 20' and crystal 30.

If desired, probe 10' may be identical to that disclosed in copending application Ser. No. 65,371 filed Aug. 20, 1970, for DENSITOMETER by C. E. Miller and G. L. Schlatter, now issued U. S. Pat. No. 3,677,067. The entire disclosure of said copending application is hereby incorporated by this reference hereto into the present application the same as though set forth in full herein hereat. The same is true of copending application Ser. No. 131,131 filed Apr. 5, 1971, for DENSITOMETER AND CALIBRATION METHOD ANDAPPARATUS THEREFOR by G. L. Schlatter, now abandoned. This application also contains some subject matter common to both of said copending applications.

The output of crystal 30' is connected to an input cir cuit 106. An amplifier 107, a squarer 108, a tracking filter 109, an amplifier 110 and a'squarer 111 are connected in succession from circuit 106 to a differentiator 102. Outputs of the differentiator 102 are connected to a synchronous detector 112 and to a linearization circuit 100, respectively. Synchronous detector 112 also receives an input over a lead 113 from the output of amplifier 107. The output of the synchronous detector 112 controls a switch 114 connected between linearization circuit 100 and utilization means 115. An adjustable frequency oscillator 116 is connected to the input of amplifier 107. A self-start circuit 117 is connected from synchronous detector 112 to squarer 108. The output of squarer 108 is impressed over a lead 118 on input circuit 106, and over a lead 1 19 on a phase detector 120. Phase detector 120 receives a second input on a lead 121 connected from the output of squarer 111. A filter frequency control circuit 122 is connected from the output of phase detector 120 to the control input of tracking filter 109. The output lead 123 of circuit 122 forms both the control input of filter 109 and the filtered output thereof, as will be'described.

A driver amplifier 124 is connected from another output of filter 109 and from the output of amplifier 100 to driver 104.

As will be explained, input circuit 106 contains a differentiator which produces an output signal 90 out of phase with the output signal of crystal 30'. The output signal of tracking filter 109, intoducedto amplifier 110, is also 90 out of phase with the input signal to tracking filter "109 from squarer, 108. Thetwo 90" phase shifts produced in input circuit 106 and tracking filter 109 can help or make it possible to connect the output of driver amplifier 124 to driver 104 in a manner to obtain resonance. That is, vane is vibrated, at its natural resonant frequency by energizing coil 24' with a level shifted alternating voltage in phase with the output of crystal 30'. The current flowing in coil 24 may be a levelshifted sine wave, but it always flows in one direction only.

As will be explained, lead 118 supplies an isolated source of potential to input circuit 106.

Oscillator 116 is employed in calibration, as will be explained.

Circuit 117 is employed to insure selfstarting. Synchronous detector 112 causes switch 114 to clamp the output of circuit 100 to a constant value when resonance does not occur.

Utilization means 115 may take any of several desired forms. When switch 114 passes the output of circuit 100, this output is directly proportional to the density of the fluid in which the probe 10 is submerged. Utilization means 115 may thus be 'a voltmeter or am meter calibrated in density, as desired. Alternatively,

utilization means 115 may be a process controller or otherwise. 1

Tracking filter 109 and linearization circuit 100 may have multiple ranges, if desired. This means that the resonant vibration of vane 20' may occur anywhere within two or more bands depending upon in what fluid vane 20' is submerged. If such is the case, it is desirable for self-start circuit 117 to produce an output signal of a frequency which changes throughout a band of interest. Switching may be employed to switch the range of the frequency sweep of the output signal of circuit 117, if desired. However, as disclosed hereinafter, the fre quency of the alternating output signal of self-start circuit 117 may vary from the lowermost limit of the lowermost band of operation of tracking filter 109 to the uppermost limit of the uppermost band of tracking fil ter 109.

The densitometer of FIG. 7 is, at least in part, an electromechanical oscillator. The crystal is the pickoff, the output of which is amplified and impressed upon driver 104. However, there is, at times, due to the absence of pipe noise and otherwise, difficulty in starting the said electromechanical oscillator. The self-start circuit 117 automatically starts vane 20 vibrating at its natural resonant frequency for the density of the fluid in which it is submerged.

Self-start circuit 117, as will be described, may include two oscillators. One of the oscillators oscillates at a lower frequency than the oscillation frequency of the other oscillator. The higher frequency is thus frequency modulated in sinusoidal, saw-tooth or any other similar periodic wave fashion. When resonance is reached, self-start circuit 117 is turned off by the output of synchronous detector 112.

Driver amplifier 124 receives an' additional input over a lead 464 from tracking filter 109. The input on lead 464 adjusts the phase of the alternating component of the output signal of driver amplifier 124 and by a simple resistor-connection, unexpectedly makes the alternating component in phase with the output signal of crystal 30' over a band of frequencies of, for example, from 2.0 to 5.0 kilohertz.

According to an outstanding feature of the invention, the driver amplifier l24 imp resses a signal on driver 104 having an alternating component which is in phase with the output signal of crystal 301. From a review of FIGS. 1-6, it will be apparent that the substantialbenefit obtained by this kind of drive is by no means obvious. The advantageis that resonance occurs, at maximum efficiency. That is, when the output voltage of driver amplifier 124 has an alternating component in phase with the output of crystal 30', the amplitude of the output of crystal 30' is a maximum. This is true even though thealternating component of the current through coil 24 lags the alternating component of the input to driver 104 by about and this current phase does not change substantially throughout, for example, an entire frequency range of 2.0 to 5.0 kilohertz.

Driver amplifier 125 also has a voltage and current offset, to be described. This makes the output of crystal '30 of the same frequency as that of the output of driver amplifier 124. The current in coil 24 always flows in one direction. That is, it is; more or less pulsating D.C. Typically, the output voltage of driver amplifier 125 is a sine wave having a peak'voltage of about 25 volts, but an average value of from, for example, about 0.1 to 0.2 volt.

Another feature of the invention to be described includes means for maintaining the average value of the current in coil 24' constant and independent of its impedance or resistance. Reliable operation is thus assured even at cryogenic temperatures. This overcomes the problem of the DC. resistance of the coil 24 dropping considerably at cryogenic temperatures.

Notwithstanding the foregoing, it will be appreciated that the densitometer of the present invention may be used to produce an output directly proportional to density. The density of either gas or a liquid may thus be obtained. Linearization circuit 100 may be used both for liquid or gas measurement. However, linearization circuit 100 is as accurate for one as the other, and this has not been possible in the prior art.

The densitometer of the present invention may be used in providing an analog voltage or current directly proportional to either gas or liquid density for any purpose, i.e., control, indication or otherwise.

OPERATION OF THE DENSITOMETER SHOWN IN I FIG. 7

In the operation of the densitometer of FIG. 7, calibration is accomplished by adjustment of oscillator 116 as will be described. Operation is then started when power is supplied. Circuit 117 then supplies an alternating output signal to squarer 108 which varies in frequency over a range of the instrument. When resonance is found, synchronous detector 112 gates off the output of circuit 117 and tracking filter 109 follows the resonant signal. The output of tracking filter 109 is impressed upon driver amplifier 124 through amplifier 110 to cause the said electromechanical oscillator to oscillate. Vane will then vibrate in one of its modes of vibration at a frequency-which is a function of the density in which it is submerged. Linearization circuit 100 then produces an output voltage and/or current analog directly proportional to density.

Switch 114 may provide a zero or other voltage or current to utilization means 1 15, if desired, during such times that resonance does not occur. On an indicator, it thus can, be determined that the instrument is not properly indicating density. Synchronous detector 112 produces an output signal. This selfsame output signal may be employed to operate both switch 114 and to start and stop self-start circuit 117.

If FIG. 8 is placed immediately to the left of FIG. 9, it will be noted that the leads fit together. For example, amplifier 126 is duplicated in both FIGS. 8 and 9 for clarity. The same is true of lead 127 and lead 128.

In FIG. 8, input circuit 106 is shown connected from crystal 30. Also shown are amplifier 107, squarer 108,

circuit 117, synchronous detector 112 and differentiator 102.

In FIG. 9, tracking filter 109 is shown with circuit 122, amplifier 110, phase detector 120, squarer 111 and driver amplifier 124.

In FIG. 8, input circuit 106 is connected from crystal 30' at junctions 129 and 130. A capacitor 131 and a resistor 132 are connected from junction 130 to ground. A differential amplifier 133 has a plus input 134 and a minus input 135. A feedback resistor 136 is connected from the amplifier output to the minus input 135. A resistor 137 and a capacitor 138 are connected from the minus input 135 to junction 130. A resistor 139 is con nected between junctions 129 and 130.

Input circuit 106 has power input terminals 140 and 141 connected from the output of amplifier 126 over a lead 142 and lead 127 to a transformer 143. Transformer 143 has a primary winding 144 connected from lead 127, and a secondary winding 145 with its ends connected to terminal 140 through diodes 146 and 147. Secondary 145 has a center tap 148 connected to terminal 141. A capacitor 149 is connected between terminals 140 and 141 to reduce the ripple. A resistor 150 is connected from junction 129 to terminal 140. A capacitor 151 is connected between terminal 140 and junction 130. A lead 152 connects terminal 141 to junction 130. The output of the circuit 106 is transformer coupled at 153 to an amplifier 154 in box 107 through a resistor 155 a nd diodes 156 and 157. Amplifier 154 has a feedback resistor 158. Squarer 108 is connected from the output of amplifier 154, and includes a coupling capacitor 159, a bias resistor 160, a bias resistor 161 and diodes 162 and 163. A resistor R1 and a capacitor C1 are connected in series in that order from the output of amplifier 133 to one end of the primary winding of transformer 153.

Amplifier 107 has a coupling capacitor 164 and a series resistor 165 connected from oscillator 116.

In FIG. 8, self-start circuit 117 is again shown connected from output lead 194 of synchronous detector 112, and connected to junction 188 in squarer 108. Self-start circuit 117 includes an oscillator 465 connected from an oscillator 466 to a gate 467. The outputs of both oscillators 465 and 466 are periodic. These outputs may be sine wave, saw-tooth or other periodic waves. The frequency of oscillator 466 is lower than that of oscillator 465. The frequency of oscillator 465 varies in accordance with the amplitude of the output signal of oscillator 466. The output of oscillator 465 is impressed upon squarer 108 through gate 467. Gate 467 is open or closed based upon whether the output signal of synchronous detector 112 is high or low. Gate 467 is connected from the said output lead 194 of synchronous detector 112.

Synchronous detector 112 is connected over a lead 189 from the output of amplifier 154. Waveform 190 is applied to detector 112 through a diode 191 over a lead 192. This causes the signal indicated at 193 on lead l89.to be sampled. If there is peak detection, an output appears at a lead which is connected to a transistor 195 through a resistor 196 and a diode 197, as shown in FIG. 10. If there is peak detection, transistor 195 does not shunt the amplifier 198 to ground. Conversely, when there is peak detection, diode 551 does not clamp input 524 of amplifier 521 to potential V1.

In detector 112 in FIG. 8, sampling is accomplished by a field effect transistor 199 across which a resistor 206 is connected.

The output of field effect transistor 199 is connected to an amplifier 201 through a resistor 202 and shunt capacitor 203. Amplifier 201 has a feedback resistor 204. Amplifier 201 has a plus input lead 205, and a minus input lead 206. Plus input lead 205 is connected to ground through a resistor 207, and to potential V2 through a resistor 207'.

Differentiator 102 includes a capacitor 208 connected in series with lead 128, a resistor 209 and a transistor 210. Transistor 210 has a base 211, a collector 212 and an emitter 213. Base 211 is connected from resistor 209. Emitter 213 is grounded. Collector 212 is connected to a positive source of potential through a resistor 214. A lead 215 is connected from collector 212 to linearization circuit 100. That is, lead 215 is the same as that shown in FIGS. 11 and 12.

As will be explained, filter 109 may be controlled to operate within two band limits.

Throughout the drawings, V2 may be 24 volts, and V1 may be l2 volts. However, theory of operation may be better understood by assuming V2, V1 and ground as shown in the drawings to be +12 volts, ground and -l2 volts, respectively. p

In FIG. 9, filter 109 includes a transitor 216 having a collector 217, an emitter 218 and a base 219. A resistor 220 is connected from lead 127 to base 219. A diode 221 is connected from base 219 to emitter 218. Emitter 2l8is maintained at potential V1. A resistor 222 is connected from collector 217 to potential V2. A resistor 223 and a capacitor 224 are connected from collector 217 to the minus input 225 of an amplifier 226. The plus input 227 of amplifier 226 is connected to potential V1. A feedback capacitor 228 is connected from junction 229 to the output of amplifier 226. A feedback resistor 228 is connected across amplifier 226. Filter 109 has a junction 229 which is connected to junction 230 in circuit 122 by a lead 231. A singlepole, double-throw switch 232 has contacts 233 and 234 and a pole 235. Potentiometers 236 and 237 are connected from junction 230 to contacts 233 and 234, respectively. A single-pole, double-throw switch 238 has contacts 239 and 240 and a pole 241. A potentiometer 242 and a resistor 243 are connected from junction 230 to contact 239. A potentiometer 244 and a resistor 245 are connected from junction 230 to contact 240. The pole 235 is connected to potential V1. The input to circuit 122 is provided by phase detector 120 on a lead 246 to an amplifier 247 through resistors 248 and 249. A capacitor 250 is connected from the junction of resistors 248 and 249 to potential VI. A potentiometer 251 having a winding 252 and a wiper 253 is connected from potential V2 to ground. A resistor 254 and a capacitor 255 are connected from wiper 253 to the output of amplifier 247. Resistors 249 and 254 are connected together by a lead256. Circuit 122 hasa field effect transistor 257 including a drain 258, a source 259 and a gate 260. A resistor 261 is connected from the outputof amplifier 247 to gate 260. Source 259 is connected to potential V1. Drain 258'is connected to pole 241.

In amplifier 110, an amplifier 262 is connected from junction 230 through a capacitor 263 and a resistor 264. Amplifier 262 has a feedback resistor 265.

Squarer 111 includes simply an amplifier 266 driven to saturation. The output of amplifier 126 is impressed upon phase detector 120 on a lead 267 connected to resistors 268 and 269, resistor 269 being connected to potential V1. Phase detector 120 has a field effect transistor 270 with a drain 271, asource 272 and a gate 273. Drain 271 is connected from resistor 268. A resistor 274 connects resistor 268 to gate 273. A diode 275 is connected from the output of amplifier 266 to gate 273. Source 272 is connected to lead 246.

Driver amplifier 124 is shown in FIG. 9. It is connected from amplifier 110 over a lead 276. It is also connected from amplifier 226 in tracking filter 109 over a lead 469. The outputof driver amplifier 124 is connected across coil 24. r f

As shown in FlG. 9, driver amplifier 124 includes resistors 470 and 471 connected respectively from leads 276 and 469 to a junction 472. A resistor 473 is connected from junction 472 to ground. The minus input to amplifier 474 is connected from junction 472. The plus input to amplifier 474 is connected from potential V1. The output of amplifier 474 is connected to the minus input of amplifier 475 through resistor 476. The plus input to amplifier 475 is connected to potential VI. A resistor 477 is connected from the minus input of amplifier 475 to the output thereof. Junction 472 is connected to the minus input of amplifier 474 through a junction 478. A resistor 479 and a capacitor 480 are connected in that order from junction 478 to the out put of amplifier 475. Coil 24 is connected between the output of amplifier 475 and a junction 481. A resistor 482 is connectedfrom junction 481 to potential VI. A resistor 483 is connected between junctions 478 and 481.

The driver amplifier 124, shown in FIG. 9, has several outstanding advantages. In the first place, it supplies a voltage to coil 24' which has an alternating component in phase with the output of crystal 30'. Moreover, the output voltage of driver amplifier 124 has an average value which is not zero. Even though it may be only 0.1 volt or 0.2 volt, this offset voltage completely prevents a current reversal in coil 24'. For example, if current flows in coil 24 in the direction indicated by arrow 484, current will never flow in a direction opposite the direction of arrow 484. This is generally true. Only a small level shift in the A.C. component of the coil voltage is necessary because the DC. resistance of coil 24' is substantially less than the AC. im-.

pedance thereof. For example, the DC. resistance of coil 24' may be 14 ohms. The resistance of resistor 482 may be, for example, 1 ohm. The capacitance of capacitor 480 may be relatively large, e.g. 0.1 microfarad.

The additional input on lead 469 effectively shifts the phase of the signal on lead 276. Note will be taken that the signals on leads 276 and 469 will generally be sine waves. Thus, when sine waves of different phases are added together, the resulting wave is a sine wave whose phase is different from the phases of both the waves which have been added together. The driver amplifier 124 effectively adds the waves on leads 276 and 469 together. The phase shift produced by the addition of the wave on lead 469 is de'sirableto compensate for the effective or ineffective operation of circuit elements or phase shifts therethrough. lt is unexpected and an outstanding advantage of the present invention that the simple addition of waves,as aforesaid, makes the input voltage to coil 24' in phase with the output signal of crystal 30' over a band of frequencies of, for example, 2.0 to 5.0 kilohertz.

As stated previously, driver amplifier 124 impresses "an alternating voltage on coil 24, the average value of which is not zero, but is only a small fraction of the peak voltage. However, the average value of the current through coil 24 is preferably equal to or somewhat larger than the amplitude of the alternating component of the coil current. The current is kept flowing in one direction only by the single resistor 483 with the resistor 482 acting to produce a voltage thereacross directly proportional to the current flowing in coil 24'.

Typically, this offset voltage is between about 0.1 volt and 0.2 volt. The feedback connection of resistor 483 with resistor 482 keeps the current in coil 24' constant at a value of, for example, to 1 50 milliamperes. Typically, coil 24' has a DC. resistance of from 10 to 15 ohms. R'esistor 479 and capacitor 480 form a feedback circuit which holds the alternating component of the voltage across coil 24' constant at, e.g. 25 volts peak.

In FIG. 11, linearization circuit 100 of FIG. 7 is shown including a pulse former circuit 13, a first integrator 15, a second integrator 16 and a sample and hold circuit connected in succession.

As shown in FIG. 12, pulse former circuit 13 includes a squarer 22, a frequency divider 23, an AND gate 14, a predetermined counter 24 and a flip-flop 25, all of which are connected from differentiator 102 in FIG. 7 to a switch 26 in FIG. 14. The 1 output of flip-flop 25 is connected to an input lead 27 of switch 26. All the switches 26, 31, 32, 33 and 19, shown in FIGS. 14, and 16, may be electromechanical or electrical, but preferably are electronic switches including, but not limited to, transistor switches. Thus, for example, the signal on input lead 27 of switch 26 closes switch 26 when the 1 output of flip-flop 25 is high.

A burst oscillator 29, shown in FIG. 12, is connected to a second input of gate 14. The 0 output of flip-flop 25 is connected to a third input of gate 14. The output of gate 14 is connected to the input of counter 24 in FIG. 12. An inverter 30 is connected from lead 28 to the reset input of flip-flop 25. The output of inverter 30 is 'alsoconnected to the reset input of counter 24.

The operation of the pulse former circuit 13 of FIG. 12 may, perhaps, be best understood from the waveforms shown in FIG. 17. Pulse former circuit 13 converts waveform (a) to waveform (d). The output of divider 23 is indicated by waveform (a). The output of gate 14 is indicated by waveform (b). Gate 14 passes a burst of pulses from oscillator 29 to counter 24 over a period which may be called T /2. The high output of divider 23 keeps gate 14 open. Initially, flip-flop 25 is in the 0 state and thus does not inhibit gate 14. Counter 24 then counts up the pulses in a burst and stops counting a period of time T,/2 after the leading edge of each output pulse ofdivider 23. Counter 24 may be adjustable as to its predetermined count, if desired. Burst oscillator 29 produces pulses at a highly stable, constant high frequency.

Once the burst of pulses has been counted, counter 24 sets flip-flop 25 to the 1 state. The 0 output of flipflop 25 then goes low and inhibits gate 14. No further pulses are then introduced to counter 24 until the leading edge of the next output pulse from divider 23. The output of inverter 30 is shown in waveform (c). When waveform (a) goes low, waveform (6) goes high, and both counter 24 and flip-flop 25 are reset. The 1 output of flip-flop 25 is thus illustrated in waveform (d).

As will be evident from the following description, the vertical input leads to switches 26, 31, 32, 33 and 19, shown in FIGS. 14, 15 and 16, represent the actuating input leads. As described previously, the actuating input lead carries a voltage which, when high, causes the switch to close. Switch 26 has an arm 34 and a contact 35. A constant voltage, E is connected to arm 34. A resistor 36 is connected between contact 35 and one input of a differential amplifier 37. The other input of differential amplifier 37 is connected to a constant voltage, +E, The input to switch 26 on lead 27 is connected from the 1 output of flip-flop 25, shown in FIG. 12, as stated previously. The output of amplifier 37, in FIG. 14, is connected to an input lead 38 connected to an arm 39 of the switch 32, switch 32 having a contact 40.

The counter 24, as shown in FIG. 13, may have either one or two predetermined counts determined by the position of single-pole, double-throw switch 106'. Two AND gates 107' and 111' are provided for two different corresponding counts.

In FIG. 14, first integrator 15 is shown including a differentiator 41 connected from lead 27 to a monostable multivibrator 42. The output of multivibrator 42 is connected to the actuating lead 43 of switch 31. The output of multivibrator 42 is also connected to an input lead 44 of a delay device 18 shown in FIG. 15, and to an actuating input lead 45 of switch 19, shown in FIG. 16.

In FIG. 14, switch 31 has an arm 46 and a contact 47. A capacitor 48 is connected from the output of amplifier 37 to the one input thereof to which resistor 36 is connected. Arm 46 is connected to the said one input of amplifier 37, and contact 47 is connected to the out put thereof.

In the operation of the first integrator 15, shown in FIG. 14, the input to switch 26 on lead 27 closes switch 26 each time and a length of time that flip-flop 25 is in the 1 state. That is, switch 26 is closed during the widths of the pulses indicated in waveform (d). The integrator of FIG. 14, therefore, integrates during at least a portion of this time. However, due to the fact that integration is performed not only during the pulses of waveform (d), but also during the time between those pulses, one of the first and second integrators 15 and 16 of FIGS. 14 and 15, respectively, must be reset during its own integration interval. It is during this interval of the first integrator that such resetting takes place.

Differentiator 41 produces an output pulse at the leading edge of each of the pulses in waveform (d). Multivibrator 42 then produces an output pulse having a leading edge coinciding with the leading edge of each of the pulses of waveform (d) and having a trailing edge occurring before the trailing edges of the pulses of waveform '(d). The output of multivibrator 42 is indicated by waveform (f) in FIG. 18. Waveform (e) is the same as waveform (d) although the scale thereof has been changed for clarity.

Receipt by switch 31 of the output of multivibrator 42 causes the capacitor 48 to discharge. Capacitor 48 is thus shunted through switch 31.

If capacitor 48 were completely discharged, at a time, t,, shown in FIG.'18, the integrator would integrate from the zero line, V starting at time, t,. Since it is the object of the integrator of FIG. 14 to produce a maximum output at a time, t which is directly proportional to the time width of pulse 49, shown in FIG. 18, an error would be introduced because the time (2 t would be omitted.

In accordance with the device of thepresent invention, this error is eliminated by preventing the output of amplifier 37 from falling below a predetermined constant voltage, E,,. This is done by supplying a suitable bias to amplifier 37, i.e. Em. This provides the bias sufficient to maintain E St where S is the slope of line 50, and t t, t Note that the line 50 thus extends precisely through the point t V, and makes the integration accurate for the entire width of pulse 49.

In accordance with the foregoing, as shown in FIG. 18, the output of amplifier 37 drops along the line 51, integrates along the line 50 and remains constant at 52 a 13 over a period between the trailing edge of pulse 49 and the leading edge of pulse 53. The output of amplifier 37 remains constant during the interval along the line 52 because during this period switch 26 is opened.

In FIG. 15, second integrator 16 is shown including an input lead 54 connected from the 1 output of flipflop 25. An inverter 55 is connected from lead 54 to the actuating input lead 56 of switch 32. As stated previously, input lead 38 is connected from the output of amplifier 37. A resistor 57 is connected from switch contact 40 to one input of an amplifier 58. The other input is maintained at potential V1 at 59. As before, a capacitor 60 is connected from the output to the input of amplifier 58 which is connected to resistor 57. A delay device 18 is connected from an input lead 44 to an actuating input lead 61 of switch 33. Switch 33 has a pole 62, and a contact 63. Pole 62 is connected to the said one input of amplifier 58. Contact 63 is connected to the output thereof. The output of delay device 18 is indicated by waveform (i) in FIG. 18. However, the pulse width and location of the output pulses of delay device 18 need not beexactly the same as that of waveform (i).

Since reset occupies a portion of the widths of pulses 49 and 53 for the first integrator 15 of FIG. 14, no special precautions need be taken in connection with the second integrator 16 of FIG. 15. Thus, the output pulses of delay device 18 provide for reset. The outputs of amplifiers 37 and 58 are shown in waveforms (g) and (h), respectively. Theoutput of amplifier 58 drops to zero volts at 64 on a line 65 produced by reset pulse 66. The output of amplifier 58 then stays at zero volts between t3 and t and integrates from to t,. The inverted pulse input on lead 56 terminates the integration and the output of amplifier 58 remains constant at the line 67 between times and t First and second integrators l5 and 16, respectively, effectively integrate for periods from t to t and from to t,, respectively. Thus, switch 26 is closed fro the period time to 1 and switch 32 is closed from t to 4. v i i v First integrator 15', shown in FIG. 14, integrates at a rate directly proportional to the constant voltage, E

7 Thus, second integrator 16, shown in FIG. 15, integrates at a rate directly proportional to the voltage upon input lead 38, this voltage being the output voltage of amplifier 37 in FIG. 14. The voltage on input lead 38 is integrated between t and t because switch 32vis closed during this time.

Sample and hold circuit 10 is shown in FIG. 16 including switch 19 having an arm 68 and a contact 69. An input lead 70 to switch 19 connected from the output of amplifier 58 is shown in FIG. 16. Switch 19 has an actuating input lead 45 connected from the output of multivibrator 42, shown in FIG. 14. The sample and hold circuit 10 of FIG. 16 thus samples the amplitude of waveform (it) between t and 1 between t, and 1 etc. Note that switch 19 is closed over the duration of therpulses of waveform (f). The entire circuit 10 of FIG. 16 may be conventional. A capacitor 71 is connected from switch contact 69 to potential V]. An amplifier 72 has one input connected from switch contact 69 and another input which is connected to potential V1 over a lead 73. i

The invention produces a DC. voltage at the output of circuit 10 directly proportional to the difference between the density of the fluid in which the desitometer probe is immersed, and a known, constant density.

If f is the resonant frequency of the vane 20', period, T, can be defined as, v

T l/f The densitometer of the present invention very accurately reproduces the equation,

d AT B where,

d is density, and, A and B are constants.

If d, is some known, fixed density for a period, T then,

Subtracting equation (3) from equation (2),

d-d,=A (T T,

Factoring and dividing by four,

d d, 4A (T/2 T,/2) (T/2 T,/2)

In FIG. 17, the output of divider 23 is indicated at waveform (a). Note that each pulse has a period, T, and that each pulse has a width T/2. In effect, pulse former l3 subtracts a known, constant pulse widthfrom the first portion of each of the pulses (a). Call this portion T /2. The output pulses of gate 14 are shown at (b). Waveform (c) is (a) inverted. Pulses (d) appear at the output of pulse former l3.

lflote that the periodbetween the trailing edges of pulses (d) is T. The period between the trailing edge of the first and the leading edge of the next is thus,

' (T/2 T./2) (T/2 T,/2

Integrators l5 and 16 thus perform the computation,

( T/ I /2 Tr/ which is directly proportional to d d By adding the known constant, d,., it is possible to arrive at absolute density.

Use of d, makes possible a more accurate computation and signal transmission because only the difference d d, is computed and transmitted; and not absolute density, d. v

Note that,

d= A (T2 T3 +d,

where,

d. AT, B

Equation (8) gives the output of amplifier 72 in terms of a voltage directly proportional to d.

The circuit of FIG. is referred to herein as switch 114. However, the circuit of FIG. 10 performs other functions than simply switching. The circuit of FIG. 10 has input leads 500 and 501, and input junctions 502 and 503. A resistor 504 is connected between input lead 500 and junction 502. A resistor 505 is connected between input lead 501 and junction 503.

Although all of the structures shown in the drawings may be employed for producing an analog signal directly proportional to fluid density, if desired, all of the structure in FIG. 19 may be omitted, in some cases, where the density of a liquid is to be measured or a density analog is desired. If the structure shown in FIG. 19 is omitted, resistor 504 can be omitted and disconnected from junction 502, the circuit of FIG. 10 other wise being left in tact.

Notwithstanding the foregoing, it is anoutstanding feature of the present invention that, especially for producing an analog directly proportional to gas density, the circuit of FIG. 19 is employed with resistor 504.

The circuit of FIG. 19 may be employed, or any conventional sampling and hold circuit may be employed. Note will be'taken that, essentially, the circuit of FIG. 19 is a sample and hold circuit. The circuit of FIG. 19 includes a sampling switch 506, an amplifier 507 having plus and minus inputs 508 and 509 respectively connected with a junction 510 and a junction 511. Junction 511 is connected to potential V1 through a winding 512 of a potentiometer 513 having a wiper 514. The operation of switch 506 is controlled by the signal on an input lead 515. Switch 506 receives an input signal on an input lead 516. Switch 506 has an output 517 connected to junction 510. A capacitor 518 is connected from junction 510 to protential V1. Junction 511 is connected from the output of amplifier 507. Switch operating lead 515 is connected from lead 56 in FIG. 15. Lead 516 is connected from the output of amplifier 37 in FIG. 14. The output of the circuit in FIG. 19 is taken from potentiometerwiper 514 and is connected to input lead 500 in FIG. 10.

The output of amplifier 72, in FIG. 16, is connected to input lead 501 in FIG. 10.

In FIG. 10, amplifiers are indicated at 519 and 520.-

Amplifier 519 has plus and minus inputs 521 and 522. Amplifier 520 has plus and minus inputs 523 and 524, respectively. A junction 525 is connected from the output of amplifier 519. Amplifier input 521 is maintained at potential V1 by a connection through to a resistor 526. A feedback resistor 527 is connected between junctions 502 and 525.

A potentiometer 528 is provided having a winding 529 and a wiper 530. One end of winding 529 is connected to potential V2. The other end of winding 529 is connected to potential V1. Wiper 530 is connected to junction 503 through a resistor 531.

Transistor 532 is provided having a collector 533, an emitter 534 and a base 535. A- diode 536 is provided having an anode 537 and a cathode 538. A junction is provided at 539. Base 535 and cathode 538 are connected from junction 525. Collector 533 is maintained at potential V2 through a resistor 540. Emitter 534 and anode 537 are connected to junction 539.

In FIG. 10, another input lead is provided at 541.

' This input lead is connected from the output lead 194 of synchronous detector 112.

In FIG. 10, junctions are provided at 542, 543, 544, 545, 546, 547 and 548. A diode 549 is connected from potential V1 to junction 542 and poled to be conductive toward the junction. A resistor 550 is connected from the said lead 194 to junction 542. A diode 551 is connected from junction 543 to junction 542 and poled to be conductive in a direction toward the junction 542. Junction 543 is connected to minus input 524 of amplifier 520. The'plus input 523 of amplifier 520 is connected to potential V1 through a resistor 552. A resistor 553 is connected between junctions 543 and 544. Junctions 544, 545, 546 and 547 are all connected together. Resistors 554 and 555 are connected in series from junction 539 to junction 544 in that order. Resistors 554 and 555 are connected at a mutual junction 556. A potentiometer 557 is provided including a wind-' ing 558 and a wiper 559. Winding 558 is connected between junctions 556 and 545. Wiper 559 is connected to junction 546.

A transistor 560 is provided including a collector 561, an emitter 562 and a base 563. A transistor is also provided at 564 having a collector 565, an emitter 566 and a base 567.

The output of amplifier 520 is connected to base 563. Collectors 561 and 565 are both connected to junction 548. Emitter 562 is connected to base 567. Emitter 566 is connected to junction 547. Junction 547 is connected to potential V2 through a resistor 568.

The circuit of FIG. 10 has an output lead 569 which, relative to potential V1, is a current directly proportional to fluid density. A resistor 570 and a milliammeter 571 are connected in series from junction 548 to output lead 569.

The portion of the circuit generally indicated at 572 is an analog .voltage adder, which may be conventional, if desired. The same is true of a voltage-to-current converter 573. The portion of the circuit indicated at 574 actually does the switching described previously.

In FIG. 10, the voltage supplied on lead 500 is directly proportional to T. It is actually equal to some constant times the quantity (T/2 T,/2). l-Iowever, T, is really a constant. The voltage supplied to lead 501 in FIG. 10 is directly proportional to T It is actually proportional to the right hand side of equation ,(4), but again, T, is constant. The potential on wiper 530 supplies to constant term, e.g.B. Thus, the output of amplifier 519 is a voltage, E which is given by the equation E AT CT B, where A, B and C are constants.

Simply because it is a requirement of industry, and not for any special purpose, the circuit of FIG. 10 is employed to produce an output current through meter 571 to read zero on a percent scale going from 0 to percent when the current through meter 571 is actually 4 milliamperes. The voltage on lead 541, which disables the output of the circuit of FIG. 10 when resonance does not exist, simply forward biases diode 551 which clamps input 524 of amplifier 521 topotential V1. This causes the meter 571 to register a current below zero and signal nonresonanace. The percent for nonresonance may be anything outside the 0 to I00 is zero or, V1 when the referenceis V1. Oscillator 116 1 is then adjusted to the lowest frequency within the range desired, and potentiometer 557 is adjusted until meter 571 reads 100 percent or 20 milliamperes. Oscillator 1 16 is disconnected before the densitometer is put into use.

The word "spaced as used herein and in the claims is hereby defined to include, but not be limited to, pulse spacing from center to center. i

The word densitometer is'hereby defined for use herein and in the claims to include a device which may or may not have utilization means 115 as described herein. i V

The switches of circuit 122 and the switch 106 shown in F 10.13, may all be ganged, if desired.

From the foregoing, it will be appreciated that synchronous detector 112 provides a sensitive device to detect whether or not resonance exists At the same time, it actuates switch 114 to produce a constant output signal on lead 569 and to turn on circuit 117 when resonance does notexist.

A portion of the output of amplifier 226 is added on lead 469 to the signal on lead 276 in driver amplifier 124 in FIG. 9, asstated previously. What portion this is depends upon the magnitude of the resistance of resistor 471.

Amplifier 475 may be a noninverting amplifier. Amplifier 474 may be an inverting amplifier. A single inverting amplifier may replace both amplifiers 475 and 474. The capacitance of capacitor 480 may be 0.1 microfarad. The magnitude of the resistance of resistor 479 determines the magnitude of the A.C. output voltage of amplifier 475. The magnitude of the resistance of resistor 483 determines the average current through coil 24'.

A capacitor is not needed in parallel with resistor 482 to average the current because the voltage drop across V resistor 482 is very,'very small in comparison to the A.C. component of the voltage input to amplifier 474. The resistor 482 supplies the offsetinput voltage to amplifier 474 through resistor 483. Thisoffset which isimpressed across coil 24' is about 0.1 volt to 0.2 volt which remains relatively constant. The alternating component 'of the voltage acrosscoil 24' is about 25 volts peak.

Note will be taken that the outputof switch 114 in FIG. 7 during resonance is directly proportional to the density of the fluid in which vane 20' is submerged. In this same case, the output of switch 114 is also directly porportional to the specific gravity of the same fluid, the difference between density and specific gravity only being due to the constant factor of the density of water. Thus, for use herein and in the claims, any form of the phrase specific gravity is herebydefined to include density" and vice versa. v

Usually the constant C in the last equation is negative .and A is usually positive. 8 may be either positive or negative.

If desired, amplifier 507 may be a noninverting amplifier and amplifier72 may be an inverting amplifier, or vice versa.

Potentiometer 513 is usually setto give a fraction of the output of amplifier 507. This fraction is the ratio of C/A as calculated from three experimental tests to derive the three constants A, B and C as a function of three known densities three measured frequencies. Typically, the said fraction is .5462. i

The phrase directly proportional is hereby defined for use herein'and in the claims to include, but not be limited to, the following examples.

d=A T T3) +df then dis defined as directly proportional to T because A, T,, and d, are constants [see equation (8) and the explanationthereof].

In FIG. 17, the width of pulses (d), i.e., (T/2 T,/2), is directly proportional to T because T, is constant.

The output of amplifier 37 in FIG. 14 is directly proportional to & Et 1 during the period from t to The output pulses from inverter occur during the period t to t,. v

The period t', t is equal tol/f. The output of amplifier 58 in FIG. 15 is directly proportional to 11i. 2 to What is claimed is:

1. A device whose response is functionally dependent upon density, said device comprising: support means; a body mounted on said support means in a position to 'be vibrated within a fluid; a driver mounted on said support means and actuable to vibrate said body, said driver including electrical means; detector means mounted adjacent said body to produce an alternating output signal of a frequency equal to a resonant frequency, f, at which said body is vibrating; feedback means connected from. said detector to said electrical meansto sustain the vibration of said body at the said frequency of vibration thereof; output means connected from said feedback means for producing a series of output pulses at a pulse repetition frequency directly proportional to f; first means responsive to the output signal of said output means for producing an output signal of a magnitude directly proportional to T, where T 1/f;second means responsive to the output signal of said output means for producing an output signal of a magnitude directly proportional to T; source means for producing an output signal of a constant magnitude;

E,,,= Ar cr+a and A, B and C are constants.

2. The invention as defined in claim 6, including utilization means connected from said adder to receive said composite output signal, said utilization means indicating the magnitude of said composite output signal.

3. The invention asdefined in claim 2, wherein said utilization means includes an electrical meter calibrated in the density of said fluid to indicate the same visually.

4. A device whose response is functionally dependent upon density, said device comprising: support means; a body mounted on said support means in a position to be vibrated within a fluid; a driver mounted on said support means and actuable to vibrate said body, said driver including electrical means; detector means mounted adjacent said body to produce an alternating output signal of a frequency equal to a resonant frequency, f, at which said body is vibrating; feedback means connected from said detector to said electrical means to sustain the vibration of said body at the said frequency of vibration thereof; output means connected from said feedback means for producing a series of output pulses at a pulse repetition frequency directly proportional to f, said output means output pulses having a pulse width directly proportional to T, where T l/f; a first source of constant potential E,,; a first integrator connected from said output means and said first source to receive said output means output pulses and said potential E, for producing an output signal at a magnitude directly proportional to during a period from to t. where t is the time at the leading edge of each of said output means output pulses, t, is the time at the trailing edge thereof, and t to an inverter connected from said output means to receive said output pulses thereof for producing output pulses during each period to L a second integrator connected from said inverter and said first integrator to output signals thereof for producing an output signal directly proportional to 20 E f dr. t2 in during a period 1 to i which is shorter than the period t to a first sample and hold circuit connected from said inverter and first integrator outputs for producing an output signal of a magnitude equal to that of the output signal of said first integrator during each period 1 to t.,, said first circuit holding its output signal at a first predetermined constant magnitude during each period t to t said first magnitude being equal to the maximum magnitude of the output signal of said first integrator during periods t to immediately prior to respective periods t to t a second sample and hold circuit connected from said output means and second integrator outputs for producing an output signal of a magnitude equal to that of the output signal of said second integrator during each period t to t said second circuit holding its output signal at a second predetermined constant magnitude during each period t to 2 said second magnitude being equal to the maximum magnitude of the output signal of said second integrator during periods t to immediately prior to respective periods t to t a second source of constant potential; and an adder connected from the outputs of both of said first and second circuits and from the output of said second source for producing a composite output signal of a magnitude E where visually. 

1. A device whose response is functionally dependent upon density, said device comprising: support means; a body mounted on said support means in a position to be vibrated within a fluid; a driver mounted on said support means and actuable to vibrate said body, said driver including electrical means; detector means mounted adjacent said body to produce an alternating output signal of a frequency equal to a resonant frequency, f, at which said body is vibrating; feedback means connected from said detector to said electrical means to sustain the vibration of said body at the said frequency of vibration thereof; output means connected from said feedback means for producing a series of output pulses at a pulse repetition frequency directly proportional to f; first means responsive to the output signal of said output means for producing an output signal of a magnitude directly proportional to T, where T 1/f; second means responsive to the output signal of said output means for producing an output signal of a magnitude directly proportional to T2; source means for producing an output signal of a constant magnitude; and an adder connected from said first, second and source means to receive all of the said output signals thereof for producing a composite output signal from said adder of a magnitude, Eoo, where Eoo AT2 + CT + B and A, B and C are constants.
 2. The invention as defined in claim 6, including utilization means connected from said adder to receive said composite output signal, said utilization means indicating the magnitude of said composite output signal.
 3. The invention as defined in claim 2, wherein said utilization means includes an electrical meter calibrated in the density of said fluid to indicate the same visually.
 4. A device whose response is functionally dependent upon density, said device comprising: support means; a body mounted on said support means in a position to be vibrated within a fluid; a driver mounted on said support means and actuable to vibrate said body, said driver including electrical means; detector means mounted adjacent said body to produce an alternating output signal of a frequency equal to a resonant frequency, f, at which said body is vibrating; feedback means connected from said detector to said electrical means to sustain the vibration of said body at the said frequency of vibration thereof; output means cOnnected from said feedback means for producing a series of output pulses at a pulse repetition frequency directly proportional to f, said output means output pulses having a pulse width directly proportional to T, where T 1/f; a first source of constant potential Eo; a first integrator connected from said output means and said first source to receive said output means output pulses and said potential Eo for producing an output signal at a magnitude directly proportional to
 5. The invention as defined in claim 4, including utilization means connected from said adder to receive said composite output signal, said utilization means indicating the magnitude of said composite output signal.
 6. The invention as defined in claim 5, wherein said utilization means includes an electrical meter calibrated in the density of said fluid to indicate the same visually. 